I owned an 08 S line 1.8tfsi in 2016. Getting straight to the point, these cars are absolutely brilliant when they work. Mine was pretty well specced (heated leather, bluetooth, parking sensors, dsg, autolights etc) and offered respectable performance, the 1.8ts are pretty rare (in this form) so I doubt you'll find a decent one(let alone with a dsg) so my money would be on you likely ending up with the 2.0 or 3.2 (if its a petrol you're after which can achieve mid to high 20s) don't pay over the odds just because it comes well specced, these can still shockingly be found for more than 6k, especially with low miles.
My general view is that these are getting old now, so be prepared to deal with a multitude of small non expensive issues which is I suppose testament to the age: Condensation in the tail lights, the rear wiper (google this), replacing screen wash hoses, excessive oil consumption, leaks and rattles. 225/40/18 tyres can be pricey if you're not used to paying £90+ p/c.
As well as the minor faults, they are still capable of doing significant damage to the wallet - timing chain (£700) and the mechatronic if you're looking for an auto (around £2k). With that said, the £5k outlay for a 10 year old A3 now jumps to around £7700, should both happen during ownership which puts the value for money aspect into perspective when looking at what you could buy if you pushed that to £8k. As above, these were 'designed' in 2003... so its pretty darn old.
They look nice and generally perform well but I'd go as new as possible for the money within your performance criteria. The car will depreciate, but not the running of it.